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Research Article

A geometrically accurate deformable-body approach for the analysis of robotic and parallel-mechanism systems

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Pages 911-931 | Received 03 Sep 2019, Accepted 23 Apr 2020, Published online: 12 May 2020

References

  • Belda, K., J. Böhm, and M. Valášek. 2003. State-space generalized predictive control for redundant parallel robots. Mechanics Based Design of Structures and Machines 31 (3):413–32. doi:10.1081/SME-120022857.
  • Bi, Z., and Y. Jin. 2011. Kinematic modeling of Exechon parallel kinematic machine. Robotics and Computer-Integrated Manufacturing 27 (1):186–93. doi:10.1016/j.rcim.2010.07.006.
  • Bi, Z., and B. Kang. 2014. An inverse dynamic model of over-constrained parallel kinematic machine based on Newton–Euler formulation. Journal of Dynamic Systems, Measurement, and Control 136 (4):041001. doi:10.1115/1.4026533.
  • Briot, S., and W. Khalil. 2014. Recursive and symbolic calculation of the elastodynamic model of flexible parallel robots. The International Journal of Robotics Research 33 (3):469–83. doi:10.1177/0278364913507006.
  • Cha, S. H., T. A. Lasky, and S. A. Velinsky. 2006. Kinematic redundancy resolution for serial-parallel manipulators via local optimization including joint constraints. Mechanics Based Design of Structures and Machines 34 (2):213–39. doi:10.1080/15397730600778527.
  • Cha, S. H., T. A. Lasky, and S. A. Velinsky. 2007. Kinematically-redundant variations of the 3-R RR mechanism and local optimization-based singularity avoidance. Mechanics Based Design of Structures and Machines 35 (1):15–38. doi:10.1080/15397730601155626.
  • Chen, D. C., A. A. Shabana, and J. Rismantab-Sany. 1994. Generalized constraint and joint reaction forces in the inverse dynamics of spatial flexible mechanical systems. Journal of Mechanical Design 116 (3):777–84. doi:10.1115/1.2919450.
  • Fotland, G., C. Haskins, and T. Rølvåg. 2020. Trade study to select best alternative for cable and pulley simulation for cranes on offshore vessels. Systems Engineering 23 (2):177–12. doi:10.1002/sys.21503.
  • Grossi, E., and A. A. Shabana. 2019. Deformation basis and kinematic singularities of constrained systems. Mechanics Based Design of Structures and Machines 47 (6):659–79. doi:10.1080/15397734.2019.1610972.
  • Goldstein, H. 1950. Classical mechanics. Boston, MA: Addison-Wesley.
  • Goldenweizer, A. 1961. Theory of thin elastic shells. Oxford, UK: Pergamon Press.
  • Greenwood, D. T. 1988. Principles of dynamics. London, UK:Prentice Hall.
  • Hunt, K. H. 1983. Structural kinematics of in-parallel-actuated robot arms. Journal of Mechanisms, Transmissions, and Automation in Design 105 (4):705–12. doi:10.1115/1.3258540.
  • Jin, Y., X. Kong, C. Higgins, and M. Price. 2012. Kinematic design of a new parallel kinematic machine for aircraft wing assembly. In Proceedings of the 10th IEEE International Conference on Industrial Informatics, Beijing, China, 669–74.
  • Kratzig, W. B., and E. Onate. 1990. Computational mechanics of nonlinear response of shells. New York: Springer-Verlag.
  • Li, H., and Z. Yang. 2008. Dynamic analysis of a parallel pick-and-place robot with flexible links. In Proceedings of the ASME 2008 9th Biennial Conference on Engineering Systems Design and Analysis, Haifa, Israel, 405–11. doi:10.1115/ESDA2008-59067.
  • Li, Q., Q. Chen, and X. Yu. 2011. 3-DOF parallel mechanism with two perpendicular and nonintersecting axes of rotation. CN Patent 201110357878.7.
  • Li, Q., and J. M. Herve. 2014. Type synthesis of 3-DOF RPR-equivalent parallel mechanisms. IEEE Transactions on Robotics 30 (6):1333–43. doi:10.1109/TRO.2014.2344450.
  • Li, Q., W. Wu, J. Xiang, H. Li, and C. Wu. 2015. A hybrid robot for friction stir welding. Proceedings of the Institution of Mechanical Engineers Part C (Journal of Mechanical Engineering Science) 229 (14):2639–50. doi:10.1177/0954406214562848.
  • Li, Q., L. Xu, Q. Chen, and W. Ye. 2017. New family of RPR-equivalent parallel mechanisms: Design and application. Chinese Journal of Mechanical Engineering 30 (2):217–21. doi:10.1007/s10033-017-0045-0.
  • Mackenzie, D. 2011. Curing ill surfaces. SIAM News 44:1–12. https://www.siam.org/news/news.php?id=1874.
  • Merlet, J. P. 2006. Parallel robots. 2nd ed. Dordrecht: Kluwer Academic Publishers.
  • Mukherjee, P., B. Dasgupta, and A. K. Mallik. 2007. Dynamic stability index and vibration analysis of a flexible Stewart platform. Journal of Sound and Vibration 307 (3–5):495–512. doi:10.1016/j.jsv.2007.05.036.
  • Naghdi, P. M. 1972. The theory of shells and plates. In Linear Theories of Elasticity and Thermoelasticity, ed. C. Truesdell, 425–640. Berlin, Germany: Springer-Verlag.
  • Noor, A. K. 1990. Bibliography of monographs and surveys on shells. Applied Mechanics Reviews 43 (9):223–34. doi:10.1115/1.3119170.
  • Noor, A. K., S. H. Belytschko, and J. C. Simo. 1989. Analytical and computational models of shells. In Proceedings of the Symposium, ASME Winter Annual Meeting, San Francisco, California, United States.
  • Pappalardo, C. M., M. Wallin, and A. A. Shabana. 2017. A new ANCF/CRBF fully parameterized plate finite element. Journal of Computational and Nonlinear Dynamics 12 (3):031008. doi:10.1115/1.4034492.
  • Patel, M., and A. A. Shabana. 2018. Locking alleviation in the large displacement analysis of beam elements: The strain split method. Acta Mechanica 229 (7):2923–46. doi:10.1007/s00707-018-2131-5.
  • Piegl, L., and W. Tiller. 1997. The NURBS book. 2nd ed. New York: Springer.
  • Quintero-Riaza, H. F., L. A. Mejía-Calderón, and M. Díaz-Rodríguez. 2019. Synthesis of planar parallel manipulators including dexterity, force transmission and stiffness index. Mechanics Based Design of Structures and Machines 47 (6):680–702. doi:10.1080/15397734.2019.1615503.
  • Reddy, J. N. 2007. Theory and analysis of elastic plates and shells. 2nd ed. Boca Raton, FL: CRC Press.
  • Rezaei, A., A. Akbarzadeh, and J. Enferadi. 2010. Stiffness analysis of a spatial parallel mechanism with flexible moving platform. In Proceedings of the ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis, Istanbul, Turkey, 647–55. doi:10.1115/ESDA2010-24560.
  • Rezaei, A., A. Akbarzadeh, and M. Akbarzadeh-T. 2012. An investigation on stiffness of a 3-PSP spatial parallel mechanism with flexible moving platform using invariant form. Mechanism and Machine Theory 51:195–216. doi:10.1016/j.mechmachtheory.2011.11.011.
  • Roberson, R. E., and R. Schwertassek. 1988. Dynamics of multibody systems. Springer-Verlag.
  • Rosyid, A., B. El-Khasawneh, and A. Alazzam. 2020. Gravity compensation of parallel kinematics mechanism with revolute joints using torsional springs. Mechanics Based Design of Structures and Machines 48 (1):27–47. doi:10.1080/15397734.2019.1619579.
  • Shabana, A. A. 2016. ANCF consistent rotation-based finite element formulation. Journal of Computational and Nonlinear Dynamics 11 (1):014502. doi:10.1115/1.4031292.
  • Shabana, A. A. 2017. Geometrically accurate floating frame of reference finite elements for the small deformation problem. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-Body Dynamics 232 (2):146441931773139 2. doi:10.1177/1464419317731392.
  • Shabana, A. A. 2019. Geometrically accurate infinitesimal-rotation spatial finite elements, Proceedings of the Institution of Mechanical Engineers. Proceedings of the Institution of Mechanical Engineers, Part K: Journal of Multi-Body Dynamics 233 (1):182–87. doi:10.1177/1464419318774948.
  • Shabana, A. A. 2018. Computational continuum mechanics. 3rd ed. Chichester, UK: Wiley.
  • Shabana, A. A. 2020. Dynamics of multibody systems. 5th ed. Cambridge, UK: Cambridge University Press.
  • Shiau, T., Y. Tsai, and M. Tsai. 2008. Nonlinear dynamic analysis of a parallel mechanism with consideration of joint effects. Mechanism and Machine Theory 43 (4):491–505. doi:10.1016/j.mechmachtheory.2007.03.008.
  • Siciliano, B. 1999. The Tricept robot: Inverse kinematics, manipulability analysis and closed-loop direct kinematics algorithm. Robotica 17 (4):437–45. doi:10.1017/S0263574799001678.
  • Specht, B. 1988. Modified shape functions for the three-node plate bending element passing the patch test. International Journal for Numerical Methods in Engineering 26 (3):705–15. doi:10.1002/nme.1620260313.
  • Stolarski, H., T. Belytschko, and S. H. Lee. 1995. A review of shell finite elements and corotational theories. Computational Mechanics Advances 2 (2):125–212.
  • Stoughton, R., and T. Arai. 1993. A modified Stewart platform manipulator with improved dexterity. IEEE Transactions on Robotics and Automation 9 (2):166–73. doi:10.1109/70.238280.
  • Timonshenko, S. P. 1955. Vibration problems in engineering. New York: McGraw-Hill.
  • Ugural, A. C. 1981. Stresses in plates and shells. New York: McGraw-Hill.
  • Wahl, J. 2002. Articulated tool head. US Patent 6431802.
  • Wang, G., and H. Liu. 2018. Dynamics model of 4-SPS/CU parallel mechanism with spherical clearance joint and flexible moving platform. Journal of Tribology 140 (2):021101. doi:10.1115/1.4037463.
  • Xi, F., D. Zhang, C. M. Mechefske, and S. Lang. 2004. Global kinetostatic modelling of Tripod-based parallel kinematic machine. Mechanism and Machine Theory 39 (4):357–77. doi:10.1016/j.mechmachtheory.2003.09.007.
  • Xu, L., Q. Li, J. Tong, and Q. Chen. 2018. Tex3: An 2R1T parallel manipulator with minimum DOF of joints and fixed linear actuators. International Journal of Precision Engineering and Manufacturing 19 (2):227–38. doi:10.1007/s12541-018-0026-y.
  • Yakoub, R. Y., and A. A. Shabana. 2001. Three dimensional absolute nodal coordinate formulation for beam elements: Implementation and applications. Journal of Mechanical Design 123 (4):614–21. doi:10.1115/1.1410099.
  • Yan, S. J., S. K. Ong, and A. Y. C. Nee. 2016. Stiffness analysis of parallelogram-type parallel manipulators using a strain energy method. Robotics and Computer-Integrated Manufacturing 37:13–22. doi:10.1016/j.rcim.2015.05.004.
  • Zarkandi, S. 2011. Kinematics and singularity analysis of a parallel manipulator with three rotational and one translational DOFs. Mechanics Based Design of Structures and Machines 39 (3):392–407. doi:10.1080/15397734.2011.559149.
  • Zhang, X., J. K. Mills, and W. L. Cleghorn. 2007. Dynamic modeling and experimental validation of a 3-PRR parallel manipulator with flexible intermediate links. Journal of Intelligent and Robotic Systems 50 (4):323–40. doi:10.1007/s10846-007-9167-4.
  • Zhang, Z., T. Wang, and A. A. Shabana. 2019. Development and implementation of geometrically accurate reduced-order models: Convergence properties of planar beams. Journal of Sound and Vibration 439:457–78. doi:10.1016/j.jsv.2018.06.005.
  • Zheng, Y., and A. A. Shabana. 2017. A two-dimensional shear deformable ANCF consistent rotation-based formulation beam element. Nonlinear Dynamics 87 (2):1031–43. doi:10.1007/s11071-016-3095-4.

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